Solution: The GCF of 65 and 90 is 5MethodsHow to find the GCF of 65 and 90 using Prime FactorizationOne way to find the GCF of 65 and 90 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:What are the Factors of 65?What are the Factors of 90?Here is the prime factorization of 65:51×1315^1 × 13^151×131And this is the prime factorization of 90:21×32×512^1 × 3^2 × 5^121×32×51When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 65 and 90 by multiplying all the matching prime factors to get a GCF of 65 and 90 as 25:Thus, the GCF of 65 and 90 is: 25How to Find the GCF of 65 and 90 by Listing All Common FactorsThe first step to this method of finding the Greatest Common Factor of 65 and 90 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.Let’s take a look at the factors for each of these numbers, 65 and 90:Factors of 65: 1, 5, 13, 65Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90When you compare the two lists of factors, you can see that the common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 65 and 90 would be 5.Find the GCF of Other Number PairsWant more practice? Try some of these other GCF problems:What is the GCF of 90 and 143?What is the GCF of 106 and 86?What is the GCF of 33 and 130?What is the GCF of 51 and 35?What is the GCF of 99 and 4?